A comprehensive study on the structural properties of distance-regular graphs and their applications in secure communication networks
Sachin Sakharam Gaikwadsachingaikwad@aitpune.edu.inDepartment of Information TechnologyArmy Institute of TechnologyDighi, Pune, Maharashtra, 411015, IndiaView full profile → , G. Uma Maheswariumamahes@maher.ac.inDepartment of MathematicsMeenakshi College of Arts and ScienceMeenakshi Academy of Higher Education & Research (Deemed to be University)Chennai, Tamil Nadu, 600078, IndiaView full profile → , *Srinivasulu GogulaCorresponding authorgsrinivasulu1678@vardhaman.orgDepartment of Computer Science and EngineeringVardhaman College of EngineeringShamshabad, Hyderabad, Telangana, 501218, IndiaView full profile → , Vinay Shivajirao Nalawadevinaynalawade2007@gmail.comDepartment of AI & Data Science EngineeringS. B. Patil College of EngineeringIndapur, Pune, Maharashtra, 413106, IndiaView full profile → , Amruta Tejaskumar Mokashiamruta.mokashi2@vit.eduDepartment of Chemical EngineeringVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , A. Vanathivanathi.andiran@adityauniversity.inDepartment of Computer Science and EngineeringAditya UniversitySurampalem, Kakinada District, Andhra Pradesh, 533437, IndiaView full profile → , Varun Kumar Sharmavarun1.sharma@niu.edu.inDepartment of Biotechnology and MicrobiologyNoida International UniversityGreater Noida, Uttar Pradesh, 203201, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2026
- Published Online:
- 31 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-3077
- Pages:
- 4611–4621
Abstract
Distance-regular graphs are a highly symmetric form of graph, whose connectivity patterns are based equally on distance, and are used both in theory and practice. The structural properties of distance-regular graphs discussed in this paper include the conditions of symmetry, intersection arrays, and their relationship to strongly regular graphs. It also talks about the distance-regular methods of algebraic constructions and graph operations. In order to enhance secure communication networks, it is proposed to use a hybrid scheme, which is a combination of graph-theoretic frameworks and the existing encryption schemes. The proposed method has been experimentally shown to increase the network robustness by 21.6 and structural attack vulnerability by 18.3 compared to traditional topologies. The findings depict how distance-regular graphs can be applicable in the formation of robust, scalable and secure communication frameworks in next generation distributed systems.
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References
[1] M. Anagreh and P. Laud, “Security proof of single-source shortest distance protocols built on secure multiparty computation protocols,” Cryptography, vol. 9, no. 1, Art. no. 1 (2025), doi: 10.3390/cryptography9010001.
[2] G. Jayabalasamy, C. Pujol, and K. Latha Bhaskaran, “Application of graph theory for blockchain technologies,” Mathematics, vol. 12, no. 8, Art. no. 1133 (2024), doi: 10.3390/math12081133.
[3] Z. Chen, M. Dehmer, and Y. Shi, “A note on distance-based graph entropies,” Entropy, vol. 16, no. 10, pp. 5416–5427 (2014), doi: 10.3390/e16105416.
[4] N. Andriyanov, “Application of graph structures in computer vision tasks,” Mathematics, vol. 10, no. 21, Art. no. 4021 (2022), doi: 10.3390/math10214021.
[5] M. Palk and S. Voß, “Graph combinatorial optimization problems for blockchain transaction network analysis,” Mathematics, vol. 14, no. 2, Art. no. 345 (2026), doi: 10.3390/math14020345.
[6] S. J. Modi, A. R. Panhalkar, N. Martin, P. V. Baviskar, T. A. Wani, and E. Kholiyarov, “Exploring advanced mathematical concepts in quantum computing for algorithm enhancement,” J. Interdiscip. Math., vol. 29, no. 3, pp. 527–535 (2026), doi: 10.47974/JIM-2487.
[7] A. Koulianos and A. Litke, “Blockchain technology for secure communication and formation control in smart drone swarms,” Future Internet, vol. 15, no. 10, Art. no. 344 (2023), doi: 10.3390/fi15100344.
[8] S. Sankaran and N. Chidambaram, “Hop and 2-hop domination on honeycomb and butterfly networks,” Symmetry, vol. 18, no. 4, Art. no. 662 (2026), doi: 10.3390/sym18040662.
[9] N. Jothilakshmi, R. Sundara Rajan, I. Rajasingh, and D. A. Emilet, “Embedding of complete bipartite graphs into some special classes of chordal graphs,” J. Discrete Math. Sci. Cryptogr., vol. 29, no. 4, pp. 1661–1672 (2026), doi: 10.47974/JDMSC-2387.
[10] S. A. U. H. Bokhary, A. Kharal, F. M. A. Samman, M. E. E. Dalam, and A. Gargouri, “Efficient graph algorithms in securing communication networks,” Symmetry, vol. 16, no. 10, Art. no. 1269 (2024), doi: 10.3390/sym16101269.
[11] E. Petropoulos, “Deep learning and optimization approaches in efficient resource management in 6G communication networks using a hybrid quantum duplet-convolutional neural network model: A review,” Int. J. Adv. Comput. Eng. Commun. Technol., vol. 14, no. 2, pp. 152–157 (2025), doi: 10.65521/ijacect.v14i2.1968.
[12] V. Kuikka and H. Rantanen, “Resilience of multi-layer communication networks,” Sensors, vol. 23, no. 1, Art. no. 86 (2023), doi: 10.3390/s23010086.
[13] R. C. Poonia, R. Almakki, A. K. J. Saudagar, A. Altameem, and M. Albathan, “A detailed examination of LSTM networks for large-scale text generation with optimizing sequence models,” J. Inf. Optim. Sci., vol. 45, no. 5, pp. 1477–1486 (2024), doi: 10.47974/JIOS-1769.
